Adaptive Aeroservoelastic Control

Ashish Tewari is a Professor of Aerospace Engineering at the Indian Institute of Technology, Kanpur. He specializes in Flight Mechanics and Control, and is the single author of five previous books, including Aeroservoelasticity – Modeling and Control  (Birkhäuser, Boston, 2015) and Advanced Control of Aircraft, Spacecraft, and Rockets (Wiley, Chichester, 2011). He is also the author of several research papers in aircraft and spacecraft dynamics and control systems. He is an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA), and a Senior Member of the Institution of Electrical and Electronics Engineers (IEEE). Prof. Tewari holds Ph.D.  and M.S. degrees in Aerospace Engineering from the University of Missouri-Rolla, and a B.Tech. degree in Aeronautical Engineering from the Indian Institute of Technology, Kanpur.

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• About the Author xvSeries Editor’s Preface xviiPreface xix1 Introduction 11.1 Aeroservoelasticity 11.2 Unsteady Aerodynamics 41.3 Linear Feedback Design 71.4 Parametric Uncertainty and Variation 111.5 Adaptive Control Design 131.5.1 Adaptive Control Laws 151.6 Organization 20References 212 Linear Control Systems 232.1 Notation 232.2 Basic Control Concepts 232.3 Input–Output Representation 262.3.1 Gain and Stability 262.3.2 Small Gain Theorem 272.4 Input–Output Linear Systems 282.4.1 Laplace Transform and Transfer Function 302.5 Loop Shaping of Linear Control Systems 332.5.1 Nyquist Theorem 342.5.2 Gain and Phase Margins 362.5.3 Loop Shaping for Single Variable Systems 382.5.4 Singular Values 402.5.5 Multi-variable Robustness Analysis: Input–Output Model 422.6 State-Space Representation 422.6.1 State-Space Theory of Linear Systems 432.6.2 State Feedback by Eigenstructure Assignment 492.6.3 Linear Observers and Output Feedback Compensators 502.7 Stochastic Systems 522.7.1 Ergodic Processes 572.7.2 Filtering of Random Noise 592.7.3 Wiener Filter 602.7.4 Kalman Filter 612.8 Optimal Control 652.8.1 Euler–Lagrange Equations 652.8.2 Linear, Quadratic Optimal Control 672.9 Robust Control Design by LQG/LTR Synthesis 712.10 H2/H∞ Design 772.10.1 H2 Design Procedure 792.10.2 H∞ Design Procedure 802.11 𝜇-Synthesis 812.11.1 Linear Fractional Transformation 83References 863 Aeroelastic Modelling 873.1 Structural Model 883.1.1 Statics 883.1.2 Dynamics 913.1.3 Typical Wing Section 933.2 Aerodynamic Modelling Concepts 983.2.1 Governing Equations for Unsteady Flow 993.2.2 Full-Potential Equation 1003.2.3 Transonic Small-Disturbance Equation 1043.3 Baseline Aerodynamic Model 1063.3.1 Integral Equation Formulation 1083.3.2 Subsonic Unsteady Aerodynamics 1093.3.3 Supersonic Unsteady Aerodynamics 1143.4 Preliminary Aeroelastic Modelling Concepts 1153.5 Ideal Flow Model for Typical Section 1203.6 Transient Aerodynamics of Typical Section 1253.7 State-Space Model of the Typical Section 1263.8 Generalized Aeroelastic Plant 128References 1354 Active Flutter Suppression 1394.1 Single Degree-of-Freedom Flutter 1414.2 Bending-Torsion Flutter 1464.3 Active Suppression of Single Degree-of-Freedom Flutter 1474.4 Active Flutter Suppression of Typical Section 1534.4.1 Open-Loop Flutter Analysis 1544.5 Linear Feedback Stabilization 1574.5.1 Pole-Placement Regulator Design 1574.5.2 Observer Design 1604.5.3 Robustness of Compensated System 1624.6 Active Flutter Suppression of Three-Dimensional Wings 164References 1685 Self-Tuning Regulation 1715.1 Introduction 1715.2 Online Plant Identification 1725.2.1 Least-Squares Parameter Estimation 1725.2.2 Least-Squares Method with Exponential Forgetting 1745.2.3 Projection Algorithm 1745.2.4 Autoregressive Identification 1755.3 Design Methods for Stochastic Self-Tuning Regulators 1765.4 Aeroservoelastic Applications 176References 1806 Nonlinear Systems Analysis and Design 1816.1 Introduction 1816.2 Preliminaries 1826.2.1 Existence and Uniqueness of Solution 1836.2.2 Expanded Solution 1846.3 Stability in the Sense of Lyapunov 1856.3.1 Local Linearization about Equilibrium Point 1876.3.2 Lyapunov Stability Theorem 1896.3.3 LaSalle Invariance Theorem 1926.4 Input–Output Stability 1926.4.1 Hamilton–Jacobi Inequality 1936.4.2 Input-State Stability 1946.5 Passivity 1956.5.1 Positive Real Transfer Matrix 1966.5.2 Stability of Passive Systems 1986.5.3 Feedback Design for Passive Systems 200References 2017 Nonlinear Oscillatory Systems and Describing Functions 2037.1 Introduction 2037.2 Absolute Stability 2057.2.1 Popov Stability Criteria 2077.2.2 Circle Criterion 2077.3 Describing Function Approximation 2107.4 Applications to Aeroservoelastic Systems 2127.4.1 Nonlinear and Uncertain Aeroelastic Plant 213References 2168 Model Reference Adaptation of Aeroservoelastic Systems 2178.1 Lyapunov-Like Stability of Non-autonomous Systems 2188.1.1 Uniform Ultimate Boundedness 2198.1.2 Barbalat’s Lemma 2208.1.3 LaSalle–Yoshizawa Theorem 2208.2 Gradient-Based Adaptation 2238.2.1 Least-Squared Error Adaptation 2258.3 Lyapunov-Based Adaptation 2258.3.1 Nonlinear Gain Evolution 2288.3.2 MRAS for Single-Input Systems 2318.4 Aeroservoelastic Applications 2338.4.1 Reference Aeroelastic Model 2348.4.2 Adaptive Flutter Suppression of Typical Section 2368.4.3 Adaptive Stabilization of Flexible Fighter Aircraft 241References 2549 Adaptive Backstepping Control 2559.1 Introduction 2559.2 Integrator Backstepping 2569.2.1 A Motivating Example 2579.3 Aeroservoelastic Application 263Reference 26410 Adaptive Control of Uncertain Nonlinear Systems 26510.1 Introduction 26510.2 Integral Adaptation 26610.2.1 Extension to Observer-Based Feedback 26810.2.2 Modified Integral Adaptation with Observer 26910.3 Model Reference Adaptation of Nonlinear Plant 27310.4 Robust Model Reference Adaptation 27510.4.1 Output-Feedback Design 28510.4.2 Adaptive Flutter Suppression of a Three-Dimensional Wing 288References 29411 Adaptive Transonic Aeroservoelasticity 29511.1 Steady Transonic Flow Characteristics 29611.2 Unsteady Transonic Flow Characteristics 29911.2.1 Thin Airfoil with Oscillating Flap 30011.2.2 Supercritical Airfoil Oscillating in Pitch 30811.3 Modelling for Transonic Unsteady Aerodynamics 31011.3.1 Indicial Method 31111.3.2 Volterra–Wiener Method 31211.3.3 Describing Function Method 31311.4 Transonic Aeroelastic Plant 31611.5 Adaptive Control of Control-Surface Nonlinearity 31711.5.1 Transonic Flutter Mechanism 31911.6 Adaptive Control of Limit-Cycle Oscillation 322References 330Appendix A Analytical Solution for Ideal Unsteady Aerodynamics 331A.1 Pure Heaving Oscillation 335A.2 Küssner–Schwarz Solution for General Oscillation 336References 337Appendix B Solution to Possio’s Integral Equation for Subsonic, UnsteadyAerodynamics 339B.1 Dietze’s Iterative Solution 340B.2 Analytical Solution by Fettis 341B.3 Closed-Form Solution 344References 345Appendix C Flutter Analysis of Modified DAST-ARW1 Wing 347References 357Index 359